ssd - Is it possible that solid state drives (or any faster drive) will make common applications faster even if they are cached?

I assumed that solid state drives are insignificant after, say, Firefox is fully brought up and no important disk activity after that is going on. However, I wonder if some kind of 'cached from the disk to the CPU' activity is going on that may make solid state drives (or any faster drive) better. Then again, I suspect that may be depended only on the Bus (or some kind of cache memory drives have). Hrm..